Details

Time bar (total: 8.3s)

sample50.0ms

Algorithm
intervals
Results
10.0ms145×body160valid
9.0ms524×pre80true
9.0ms268×body80nan
4.0ms111×body80valid

simplify53.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
27.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
34.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series307.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify722.0ms

Counts
82 → 82
Iterations

Useful iterations: done (719.0ms)

IterNodesCost
01541565
14061461
213591245
done50011235

prune219.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
34.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series414.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
123.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
48.0ms
(- (* b b) (* (* 4.0 a) c))
165.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.0s

Counts
163 → 163
Iterations

Useful iterations: done (995.0ms)

IterNodesCost
02545790
16705273
223874513
done50004511

prune485.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
11×add-exp-log add-cbrt-cube
10×add-log-exp
8×add-cube-cbrt
7×associate-*r*
6×pow1
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×times-frac diff-log associate-*l* associate-/l*
2×cbrt-undiv distribute-rgt-in distribute-rgt-neg-in distribute-lft-in div-exp prod-exp sqrt-prod associate-/r/ cbrt-unprod associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ pow-prod-down neg-log clear-num associate-/r* *-commutative flip-+ div-inv unswap-sqr
Counts
4 → 83
Calls
4 calls:
44.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(/ (+ 0 (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
148.0ms
(/ (+ 0 (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify806.0ms

Counts
95 → 95
Iterations

Useful iterations: done (803.0ms)

IterNodesCost
01692004
14461830
219381604
done50011603

prune299.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* (- b) a) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (+ (* (- b) a) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×associate-*r*
9×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×pow1 distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
4×distribute-rgt-neg-out
3×flip3-+ associate-*l* associate-/r* flip-+ associate-/l*
2×flip3-- sqrt-div associate-*r/ associate-/r/ flip-- associate-/l/ distribute-neg-frac
1×cbrt-undiv +-commutative distribute-lft-neg-out neg-mul-1 sub-neg distribute-neg-out frac-2neg diff-log div-exp unsub-neg pow-prod-down prod-exp clear-num sum-log *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 91
Calls
4 calls:
3.0ms
(+ (* (- b) a) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.0ms
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (* (- b) a) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(+ (* (- b) a) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
88.0ms
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
233.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (* (- b) a) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify914.0ms

Counts
103 → 103
Iterations

Useful iterations: done (911.0ms)

IterNodesCost
02002482
15192278
219431905
done50001900

prune338.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes133.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
02330
13728
24627
34827
done4827

end0.0ms

sample1.4s

Algorithm
intervals
Results
315.0ms4520×body160valid
291.0ms16557×pre80true
289.0ms8557×body80nan
129.0ms3480×body80valid